Adaptive multiquadric collocation for boundary layer problems

AbstractAn adaptive collocation method based upon radial basis functions is presented for the solution of singularly perturbed two-point boundary value problems. Using a multiquadric integral formulation, the second derivative of the solution is approximated by multiquadric radial basis functions. This approach is combined with a coordinate stretching technique. The required variable transformation is accomplished by a conformal mapping, an iterated sine-transformation. A new error indicator function accurately captures the regions of the interval with insufficient resolution. This indicator is used to adaptively add data centres and collocation points. The method resolves extremely thin layers accurately with fairly few basis functions. The proposed adaptive scheme is very robust, and reaches high accuracy even when parameters in our coordinate stretching technique are not chosen optimally. The effectiveness of our new method is demonstrated on two examples with boundary layers, and one example featuring an interior layer. It is shown in detail how the adaptive method refines the resolution

Quantitative Approaches to Universality and Individuality in Language

Founding Editor: Gabriel Altmann The series Quantitative Linguistics publishes books on all aspects of quantitative methods and models in linguistics, text analysis and related research fields. Specifically, the scope of the series covers the whole spectrum of theoretical and empirical research, ultimately striving for an exact mathematical formulation and empirical testing of hypotheses: observation and description of linguistic data, application of methods and models, discussion of methodological and epistemological issues, modelling of language and text phenomena.Используемые программы Adobe AcrobatРедактор-основатель: Габриэль Альтманн Серия "Количественная лингвистика" публикует книги по всем аспектам количественных методов и моделей в лингвистике, анализе текста и смежных областях исследований. В частности, тематика серии охватывает весь спектр теоретических и эмпирических исследований, в конечном счете направленных на точную математическую формулировку и эмпирическую проверку гипотез: наблюдение и описание лингвистических данных, применение методов и моделей, обсуждение методологических и эпистемологических вопросов, моделирование языковых и текстовых явлений